A common model like this happens, for instance, in San Antonio, TX.
In this case, you often follow one (or small group of) surgeon(s) around and become his/her(their) "personal" anesthesiologist. You take vacation when he/she takes vacation, you go to different hospitals/surgery centers, you gotta keep him/her happy.
Upside is that you get pretty good and knowing what one (or a couple) of surgeon(s) prefers and you can develop a good rapport. Downside... well, limited case exposuire, and obviously you're always going to be someone's b*tch.
I'm sure there are other models out there, but this is the main one I've heard of with pure "fee-for-service" independent practice.
-copro